{"paper":{"title":"On the optimality of the uniform random strategy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christopher Kusch, Christoph Spiegel, Juanjo Ru\\'e, Tibor Szab\\'o","submitted_at":"2017-11-20T10:53:36Z","abstract_excerpt":"The concept of biased Maker-Breaker games, introduced by Chv\\'atal and Erd{\\H o}s, is a central topic in the field of positional games, with deep connections to the theory of random structures. For any given hypergraph ${\\cal H}$ the main questions is to determine the smallest bias $q({\\cal H})$ that allows Breaker to force that Maker ends up with an independent set of ${\\cal H}$. Here we prove matching general winning criteria for Maker and Breaker when the game hypergraph satisfies a couple of natural `container-type' regularity conditions about the degree of subsets of its vertices. This wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07251","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}